Its current presenters include former BBC journalist Simon McCoy, ex-Sky host Kirsty Gallacher, former UKIP leader Nigel Farage and ITN’s Alastair Stewart, who left ITV News last year after a Twitter row.
Sources have claimed nothing had been “formally agreed” with Eamonn and described the situation as an “early conversation”.
However, some reports have said the move was sealed.
It is also rumoured that Eamonn might end up presenting his own show on the channel a couple of times a week.
It comes after the broadcaster is claimed to have angered ITV bosses last year when he appeared to promote conspiracy theories about 5G technology and coronavirus.